When starting out, you need a base layer, then something like a fleece or pullover, and a good rain jacket. For hiking trips and day climbs where it's not really cold, that's fine. When you do expect really low temperatures, add a down jacket.

As for base layers, merino has an excellent reputation, but I don't like how it feels on my skin. You just have to try it on to judge for yourself. If it doesn't feel comfortable in the store, don't buy it. There are many other types and brands out there, and I've tried several. Most of them actually work quite well for me, cheap ones as well as the more expensive ones. Unless it's really hot, my favorite brand is Craft. It doesn't itch, keeps me dry even when I work up a bit of a sweat, and it provides some insulation as well (it's a cold weather model).

As a second layer, I don't use brand names. In my experience, it's not worth the money. If it's just a little to cold for only a base layer, I just put a second base layer on. If it's a bit colder still, many cheap fleeces do an excellent job, and a whole lot less. I got some really good ones for less than 10 Euros, and used one of those extensively all over Peru. It's relatively thick, and therefore warm. So, no Patagonia or Arcteryx for me.

You don't mention a rain jacket. I usually do buy brand names there. A good one costs at least 200 euros, often more. Cheaper ones either don't keep the rain out or don't breathe very well.I've worn down a bunch of rain jackets over the years, but the best ones I ever had were by Tenson and by Columbia. The first one got ripped to shreds on some sharp rocks in the Dolomites, the second one I either lost or it got stolen - I still don't know which. Unfortunately, in my experience, only time will tell if a jacket is really good, but the brand names don't make bad ones.

I don't know the Eddie Bauer down jacket you mention. My down jacket is a Rab Neutrino Endurance. It weighs a lot less and has kept me warm even below -20°C. I rarely need it in Europe, but it's in my pack, just in case. My boots and mittens can't handle lower temperatures anyway, so I stay in the refuge or in my tent.More importantly however, if you start out, try to avoid spending a lot of money to buy a down jacket at all. Get more experience first, and put an extra second layer in your pack on the occasional day that you expect cold weather. I had a cheap wind breaker for that for years. It provided less isolation, but in Europe that was fine. I rarely needed it. If the company where you booked your training course says you must have a down jacket, ask them about renting.

From what I read about it, the Arcteryx Atom LT is not a rain jacket. I guess it will be all right in a drizzle, or at best a short shower, but not in real rain.

Mostly I wear regular hiking pants on alpine routes. The main thing is that they dry quickly when they get wet. I've also got breathable rain pants. Neither are big brands, and when they're done, I just buy new ones. My legs don't get cold quickly, but on a very cold day, I sometimes use my rain pants as extra layer. I rarely need to though.

This setup works fine all over Europe in the summer. I've got a pair of long thermal underpants too, but I hardly ever bother to pack them. But for the highest ones, such as Mont Blanc, it's a useful precaution to have them.

That said, hiking pants are less suitable for climbing on sharp rock. One time I've shredded in the Dolomites doing that. But I could have climbed in shorts that day. If you are going to climb a lot of alpine rock routes, buying a pair of pants that can stand a lot of wear and tear would be better.

When it's really cold, I've got a pair of warm dungarees that I bought years ago. They were primarily meant for skiing and I've done that, but they are excellent for mountaineering too. I can sit in the snow for a while with them without getting a wet bottom. I don't know what kind of insulation material is in there, but it's something synthetic, no down. I never needed them while climbing in Europe, but they were fine in the Andes.

As for boots, there are loads of threads discussing that topic. You might want to check them out specifically. The short answer is that what is a good boot you is very personal. If it doesn't fit properly, it's no good, and everybody's feet are different. You just have to experiment.

As for my own boots, I've just about worn down my favorite ones, Millet Rock & Ice GTX. I've used them extensively all over the Alps as well as in a few other places. Got to buy a new pair, if I can find them. They are excellent on glacier routes and on rock, and they are comfortable enough for me to hike a long distance in them. However, they are a bit warm below the snow line.

For colder places, I've got Scarpa Omega boots. They function down to about -20°C, although I do get very cold feet when it's that cold, especially if I'm not on the move. But they fit really well, they are light and for stiff plastic boots they are easy to walk in. I've also got a big assortment of hiking boots, light and heavy, and some are suitable for crampons.

Depending on the type of terrain and the temperatures I expect, I decide which ones to pack. I go with the lightest pair that I think will be good enough. They've got to be suitable for the terrain, and not so warm that I sweat too much. When crossing glaciers or snow fields, or in wet places like Scotland, water resistance is an important consideration too. Unless it's a short trip, I usually bring two different pairs.My Scarpa Omega boots in their natural habitat

Charle wrote:And in case of boots, probably the best set will be trail running shoes + hiking boots + mountain boots.

When traveling for a longer period, that's similar to what I usually bring. But then I always leave part of my gear somewhere safe in the valley before heading into the mountains. Depending on the terrain, and on whether there are mules or porters, I decide what footwear to bring, but two pair at most.